Brush chicken breast with olive oil and sprinkle with salt and pepper. Grill on medium heat for 4 minutes per side until internal temperature reaches 165 degrees. Let rest for a few minutes and then cut chicken into bite size strips. (Chicken can alternately be baked in the oven or cooked however you so desire.)
Trim and diagonally cut asparagus into thirds. Blanch the asparagus in a pot of boiling salted water for 3-5 minutes, until crisp-tender. Plunge into ice water to stop the cooking. Drain. Cut the peppers into strips, same size as the asparagus. Combine the chicken, asparagus, and peppers in a large bowl.
Whisk together all of the dressing ingredients and pour over the chicken mixture (Note-there may be leftover dressing). Add the scallions and sesame seeds and season to taste. Serve cold or at room temperature.